The invention relates to a method for designing an electromagnetic gradient coil for magnetic resonance imaging systems comprising:    a. Choosing a set of objectives, whereby the objectives are combined to one weighted-sum objective function,    b. Choosing a design variable for modifying the value of the objectives;    c. Making an initial guess of the value of the design variable,    d. Simulating the magnetic field in a computational domain with respect to the distribution of the surface current density,    e. Carrying out a sensitivity analysis by calculating a sensitivity vector,    f. Updating the design variable whereby the value of the design variable is changed in order to decrease the value of the objective,    g. Determining whether convergency is achieved by either determining whether the value of the objective function does not decrease or the whether the Euclidian norm of the sensitivity vector approximate to zero;    h. Reconstruction of a discretized coil.
A method of this type was disclosed in [2] [3] [4] [5] [6] [7].
Magnetic resonance imaging (MRI) is a relative new technology compared with computed tomography (CT) and the first MR Image was published in 1973[1]. It is primarily a medical imaging technique which most commonly used in radiology to visualize the structure and function of the body. It could provide detailed Images of the body in any plane. MRI provides much greater contrast between the different soft tissues of the body than CT does, making it especially useful in neurological, cardiovascular, and oncological imaging. It uses a powerful magnetic field to align the nuclear magnetization of hydrogen atoms in water in the body. Radio frequency fields are used to systematically alter the alignment of this magnetization, causing the hydrogen nuclei to produce a rotating magnetic field detectable by the scanner. This signal can be manipulated by additional magnetic fields to build up enough information to reconstruct an image of the body.
In an MRI scanner there are three main parts, a static magnetic field, three orthogonal and controllable magnetic gradients, and radio frequency (RE) transmitter and receiver. The magnet is the largest and most expensive component of the scanner which is used to generate the main static magnetic field B0, and the remainders of the scanner are built around it. The straightness of the magnetic lines within the center of the magnet needs to be near-perfect. This is known as homogeneity. Gradient coils are used to spatially encode the positions of protons by varying the magnetic field across the imaging volume. The Larmor frequency will then vary as a function of position in the x, y and z axes respectively. Gradient coils are powered by amplifiers which permit rapid and precise adjustments to their field strength and direction. Typical gradient systems are capable of producing gradients from 20 mT/M to 100 mT/M. The main factors of the gradient coils are the gradient field strength and the switch time. Usually stronger gradients allow for higher resolution, and low inductance of the gradient coil allows the faster switching and faster imaging. The RF transmission system consists of a RF synthesizer, power amplifier and transmitting coil. This is usually built into the body of the scanner. The receiver consists of the coil, pre-amplifier and signal processing system. A variety of coils are available which fit around parts of the body. The design of novel gradient coils which can generate specified magnetic gradients are discussed in the following.
Currently there are two methods commonly used for designing the MRI gradient coil, the analytical method and the numerical optimization method. The differences between these two methods are mainly for the method used to calculate the magnetic field in the region of interest (ROI) with respect to the distribution of the surface current density. For the analytical type method, the magnetic field Bz is calculated using the Blot—Savart law or the series expansion if the current exists on the regular surface, such as planar or cylinder surfaces. The dominated design method for the gradient coil design is the so-called target field method [2] [3] [4] [5] [6] [7]. This method relies on the Fourier transform which is widely used for many integral equations. The ideal value of magnetic field distribution is used with the collation method to interpolate the coefficients matrix for the analytical expression of the magnetic field. The current density value is solved using the inverse of the coefficient matrix and the magnetic value on the collocation points. Because of the analytical characteristic of the target field method, the design of the gradient coil theoretically needs to solve merely one linear algebra equation. This is a big advantage compared with the most of numerical optimization methods in which the design procedure strongly depends on the iteration update, especially 20 years ago that the computer had limited computational performance.
However, the target field method also has unavoidable drawbacks. Firstly, the series expansion of the magnetic field works for the infinite open domain, whereas the gradient coil must locate in the limited domain. Therefore there exists cutoff error when the gradient coil is limited in certain length. Secondly, the special function used for the series expansion merely works properly for the regular surface. For the irregular surface or piece of regular surface (for example, a cylinder surface with a circle hole), there is no straightforward extension for the target field method. Thirdly the inverse of the coefficient matrix is ill-posed. The condition number of the matrix is strongly dependent on the number and position of the collocation points. The small numerical error introduced by the computational procedure may generate significant variation of the gradient coil and then the magnetic field Bz in ROI. In [8], authors mentioned that the best result can be obtained when the target points is imposed along the axis of the solenoid or every close to it. This means that the ROI merely has small dimension along the main magnetic field B0 direction which is contradiction with the design goal of the gradient coil which prefers as larger functional ROI as possible.
Compared with the analytical method, the numerical optimization method [9] [10] [11] has advantages in the case that the computational domain is irregular, or the objective field cannot be expressed directly using the polynomials. The computational domain is a three dimensional domain. The surface where the design variable exists (design domain) should stay inside the computational domain and should surround the ROI.
However, the numerical optimization method also has obvious drawbacks at this moment. There are a couple of the numerical methods can be used to calculate the distribution of the magnetic field, for example, the finite element method, the finite different method, the boundary element method, the method of moments, and the fast multipole method etc. For all of these numerical methods, the computational cost is much expensive than the analytical method. At the same time, the design of novel gradient coil has to be implemented using the numerical iterative type optimization methodology. This is the reasons the analytical method is still the first choice if one can use it.
Object of the present invention to suggest method for coil design based on the target field method which allows an effective and improved design for irregular surfaces and reduction of cutoff errors.